Properties

Level $9$
Weight $0$
Character 9.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 10.4711201375 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.698026059\) \(a_{3}=+0.000000000\) \(a_{4}=+1.883292496\) \(a_{5}=+1.636998807\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.168039008\) \(a_{8}=+1.499853676\) \(a_{9}=+0.000000000\) \(a_{10}=+2.779666632\)
\(a_{11}=-0.907521447\) \(a_{12}=+0.000000000\) \(a_{13}=+1.198916938\) \(a_{14}=-0.285334615\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.663498131\) \(a_{17}=+0.209938508\) \(a_{18}=+0.000000000\) \(a_{19}=+0.690216367\) \(a_{20}=+3.082947569\)
\(a_{21}=+0.000000000\) \(a_{22}=-1.540995067\) \(a_{23}=-0.507404645\) \(a_{24}=+0.000000000\) \(a_{25}=+1.679765093\)
\(a_{26}=+2.035792203\) \(a_{27}=+0.000000000\) \(a_{28}=-0.316466605\) \(a_{29}=+0.701136253\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.657672662\) \(a_{32}=-0.373216540\) \(a_{33}=+0.000000000\) \(a_{34}=+0.356481009\) \(a_{35}=-0.275079538\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.074860934\) \(a_{38}=+1.172006012\) \(a_{39}=+0.000000000\) \(a_{40}=+2.455257360\)
\(a_{41}=+0.565265665\) \(a_{42}=+0.000000000\) \(a_{43}=-0.941968892\) \(a_{44}=-1.709112349\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.861616134\) \(a_{47}=-0.486259417\) \(a_{48}=+0.000000000\) \(a_{49}=-0.971895214\) \(a_{50}=+2.852611011\)
\(a_{51}=+0.000000000\) \(a_{52}=+2.257363083\) \(a_{53}=-1.473665006\) \(a_{54}=+0.000000000\) \(a_{55}=-1.487725788\)
\(a_{56}=-0.246913986\) \(a_{57}=+0.000000000\) \(a_{58}=+1.182716025\) \(a_{59}=+0.036986082\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.667829591\) \(a_{62}=-1.056781719\) \(a_{63}=+0.000000000\) \(a_{64}=-1.382604215\) \(a_{65}=+2.138172858\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.289445316\) \(a_{68}=+0.839474943\) \(a_{69}=+0.000000000\) \(a_{70}=-1.137305465\)

Showing all 70 available coefficients

Rows: Cols: